Normalized information

Figure 8.2 Normalized Information Index of kt and k versus time to determine the best section of data to be used by the Gauss-Newton method fl tmax=0.0884, Fmas=0.0l23) [reprinted from Industrial Engineering Chemistry Fundamentals with permission from the American Chemical Society],...

From the same figures it is also seen that the normalized information indices of k and k2, as well as k and k4, overlap completely. This behavior is also not surprising since the experiments have been conducted isothermally and hence the product k evp(-k2/T) behaves as one parameter which implies that (3x,/3ki) and (px,/5kj) and consequently I (t) and I2(t) differ only by a constant factor. 

Thus, we will define the normalized information as the reciprocal of the normalized uncertainty. The normalized information is bounded between 1 and 0 ... 

The normalized uncertainty and normalized information are related to the variance function and information function, respectively, defined by Box and Draper (1987). 

One purpose of a good design is to minimize uncertainty and maximize information over the region of interest. We will use both normalized uncertainty and normalized information to discuss the effect of experimental design on the quality of information obtained from a two-factor FSOP model. 

The upper right panel shows a surface of normalized information (defined in Equation 13.8 above) as a function of factors x, and x. The normalized information is relatively large in the center (approximately 0.91) and relatively small at the comers (approximately 0.25). Note that this surface also reflects the underlying design the information is relatively high in those regions where experiments have been performed and is relatively low in those regions where experiments have not been carried out. 

The lower right panel plots normalized information as a function of factor x, for Xj = -5, -4, -3, -2, -1, and 0. These lines show the left front edge (xj = -5) and parallel slices through the normalized information surface in the panel above. (For this design which is symmetric about the x, axis, the graph lines for Xj = 1, 2, 3, 4, and 5 are identical to lines that are already present.)... 

One of the striking features of this central composite design is the flatness of the normalized uncertainty and normalized information surfaces near the center of the design. 

In Figure 13.2, the experimental design, the normalized uncertainty surface, and the normalized information surface each have four planes of mirror-image symmetry, all of which are perpendicular to the x, - Xj plane. One reflection plane contains the... 

The normalized information at the center (and at the edges) of the factor space in Figure 13.3 is less than the normalized information at the center (and at the edges) in Figure 13.2. These effects are a result of the relative compactness of the star points in this rotatable design which allows the FSOP model to flex more at the comers of the factor space and, consequently, at the center as well. 

Note that the sides of the rectangular normalized information surface have been pinched inward. The shape of this surface is clearly related to the placement of the experiments in factor space as shown in the lower left panel. A constant theme of experimental design is that generally in those regions where experiments have been carried out, there is superior information in those regions where experiments have not been carried out, there is inferior information. 

This allocation of experiments has the effect of making the normalized uncertainty and normalized information contours more axially symmetric (the design isn t quite rotatable there are still only four mirror-image planes of reflection symmetry). However, because no experiments are now being carried out at the center point, the amount of uncertainty is greater there (and the amount of information is smaller there). The overall effect is to provide a normalized information surface that looks like a slightly square-shaped volcano. 

Because each of the pentagonal points is equidistant from the center of the design, the design is rotatable. This rotatability is seen in the axially symmetric surfaces for normalized uncertainty and normalized information. 

At a very basic level, the shapes of the normalized uncertainty and normalized information surfaces for a given model are a result of the location of points in factor space simply because carrying out an experiment provides information - that is, information is greatest in the vicinity of the design. But at a more sophisticated and often more important level, the shapes of the normalized uncertainty and normalized information surfaces are caused by the geometric vibrations of the response surfaces themselves - the more rigidly the model is pinned down by the experiments and the less it can squirm and thrash about, then the less will be the uncertainty and the greater will be the information content. 

The striking feature of this design is the set of six spikes in both the normalized uncertainty and normalized information surfaces. These spikes are an extreme expression of the basic idea that experiments provide information. Even if the experimental design is not a good match for the model even if the iX X) matrix is ill conditioned even if the model doesn t fit the data very well, there is still high-quality information at the points where experiments have been carried out. 

Find a report of a two-factor experimental design. Speculate about the shape of the normalized uncertainty and normalized information surfaces for the design. Sketch their shape. 

Suppressor tRNAs constitute an experimentally induced variation in the genetic code to allow the reading of what are usually termination codons, much like the naturally occurring code variations described in Box 27-2. Nonsense suppression does not completely disrupt normal information transfer in a cell, because the cell usually has several copies of each tRNA gene some of these duplicate genes are weakly expressed and account for only a minor part of the cellular pool of a particular tRNA. Suppressor mutations usually involve a minor tRNA, leaving the major tRNA to read its codon normally. 

After rubber lining, no welding or earthing should be done on the lined tank, so the lugs, hooks, pipe supports, etc. which may be required to be welded on the vessel, piping, etc. should be planned and completed at the time of fabrication of the vessel itself. The fabricator is normally informed about this in advance. In the case of concrete... 

Another measure for accuracy is an entropy-related information, /, as defined below. It merges the different percentages to a single number with all elements of the accuracy matrix (Table 8.1) contributing equally. The advantage of such entropy is that over- and under-predictions equally decrease the value of /. The normalized information value / equals zero in a randomly distributed population (where Ay = N/9), whereas / = 1 in a perfect match between predicted and observed populations (A = b, and Ay = 0 for i =j). 

Functional Testing GAMP Forum (1996) Also known as Black Box testing, since source code is not needed. This involves inputting normal information and abnormal test cases and then, evaluating outputs against those expected. Can apply to computer system or to a total system. [Adapted.]... 

Hazardous area equipment that has been tested and approved by a recognised laboratory should have a marking plate attached to its surface, in a place easily seen by the user. This plate is usually the nameplate that shows the normal information such as the name of the manufacturer, voltage, rated power, full load current, frequency, model number, serial number, ambient temperature and date of manufacture. The additional information to be shown for the hazardous area application, should be at least the following ... 

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